Time decay of the thermoremanent magnetization in spin-glasses as a function of the time spent in the field-cooled state

Abstract

We have measured the time decay of the thermoremanent magnetization (${\sigma }_{\mathrm{TRM}}$) in Ag: Mn as a function of the wait time ($t_w$) that the sample spent in the field-cooled state before the field was removed. When the results are analyzed in terms of a stretched exponential, ${\sigma }_{\mathrm{TRM}}\mathrm{}\left(t\right)={\sigma }_0\exp \left[\frac{-C{\left(\omega t\right)}^{1-n}}{\mathrm{}(1-n)\mathrm{}}\right]$, we find that the effect of $t_w$ can be empirically characterized as an exponential decrease of the relaxation frequency with increasing wait time: $\omega ={\omega }_0\exp \left(\frac{-t_w}{t_0}\right)$, where ${\omega }_0=3.3\mathrm{}\times {10}^{-4\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ and $t_0=650\mathrm{}$ sec. This fact has two implications, First, even though the field-cooled magnetization is constant in time, the field-cooled state is not in equilibrium for finite $t_w$. And second, if $t_w\to \infty$ then the field-cooled spin-glass will have a permanent magnetic moment.